Informally speaking, the information scrambling caused by \(U_{AB}\)  refers to the spread of input information on \(\mathcal {H}_A\)  over the output Hilbert space \(\mathcal {H}_C\otimes \mathcal {H}_D\) .
It is characterized by the information about \(A\)  nonlocally shared by the outputs \(C\)  and \(D\)  which cannot be extracted from either \(C\)  or \(D\)  exclusively.
Given the state \({\Psi }\)  (REF ), such a quantity may be represented by the negativity of the tripartite information \(I(R,C,D)\)  [1]},
\(-I(R,C,D) I(R,CD) - I(R,C) - I(R,D).\) 
